Instructions: Write $($or type$)$ clearly, staple your pages, and write $$Homework $8$ and your

name at the top of your homework. Total Points: $20.$

$1.(2$ Points$)$ Consider a system with single server to serve customers. The customers$$

arrival rate is $5$ per hour and the server$$s service rate is $10$ per hour. If we take a look of

the system at several random times, shall we observe a queue of customers in the

system? Explain the reason.

$2.(2$ Points$)$ Consider two systems with single server to serve customers. The following

two scenarios describe how the waiting time is affected by variability $($in customers$$

arrival time and service time$)$ and utilization $($utilization is the demand rate over

capacity rate$)$:

Scenario $1$: Suppose two systems have the same utilization rate. The system with

$\_\_\_\_\_\_\_\_\_($High$/$Low$)$ variability has shorter average waiting time.

Scenario $2$: Suppose two systems have the same variability. The system with $\_\_\_\_\_\_\_\_\_$

$($High$/$Low$)$ utilization has shorter average waiting time.

Hint: use the actual flow time $$ utilization graph

$3.(4$ Points$)$ Tony Soprano sits at a table in the back of Irish Lion $($a bar & restaurant$)$

waiting for visitors. If the chair opposite Mr$.$ Soprano is occupied, visitors wait at the

bar. When the chair becomes free, the next visitor sits down and talks to Mr$.$ Soprano.

Visitors arrive randomly at a rate of ten per hour. Once seated, the visitor does not leave

until Mr$.$ Soprano has finished the conversation. Mr$.$ Soprano is quite unpredictable.

The lengths of his conversations are random, and have a mean time of four minutes.

Once the conversation is over, the visitor always leaves the restaurant. Each visitor pays

to the bar manager for the time waiting in the bar. The payment rate is $$0\mathrm{.}8$ per minute.

On average how much will each visitor pay to the bar manager?

$4.(1$ Point$)$ Which of the following rules tends to minimize the average lateness?

A$.$ FCFS

B$.$ SPT

C$.$ EDD

D$.$ LPT

$5.(4$ Points$)$ Suppose that the following six jobs, listed in order of arrival, must be

scheduled through a car repair facility:

Job

Process

Time

$($days$)$

Due

Date

A $2342$

B $1318$

C $733$

D $1861$

E $2945$

F $1130$

Find the makespan, average flow time, average number of jobs in the system, and

average tardiness following the EDD rule. $(1$ Point each$)$

$6.(3$ Points$)$ Consider the following information, suppose the current day is $15,$ what is the

priority order using the Critical Ratio rule?

Job Due Date Workdays Remaining

A $175$

B $217$

C $196$

$7.(4$ Points$)$ Given the following data, how would you schedule the jobs applying

Johnson$$s Rule? What is your resulting makespan?

Job M$1$ M$2($Processing Time at Machines $1$ and $2)$

A $52$

B $54$

C $75$

D $77$

E $67$

F $34$